Linear Algebra :

• It help us to understand the higher dimesional (4D,5D etc) space using mathematical tools we need .
• It generalized the 2D and 3D to higher dimenional

• Basic Concepts in Linear Algebra :
  * Point or Vector

Distance of a point from origin :

Distance between two Points :

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Some terminology : Row vectore, Column Vector, Matrix

Matrix Operation : Vector Addition ,Vector Multiplication (Dot product, Cross product)

• Cross product is not much more used in ML

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Geomertical meaning of dot product :

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Projection and Unit Vector :

Unit Vector : It is the vector in same direction having length is unity

Equation of a line (2-D), Plane(3-D) and Hyperplane (n-D), Plane Passing through origin, Normal to a Plane -- Lecture10.5 missed

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Distance of a point from a PlaneHyperplane, Half-Spaces :

• distance of a point from a plane
• A line divides the 2-D space into two parts
• A plane divided the 3-D space into two parts
• A hyper-plance divides the 4-D or higher dimensional space into two parts , these two parts are called hyper-space

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Equation of a circle(2D), Equation of Sphere(3D), Equation of Hypersphere(n-D):

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Q .How to determine a point is inside circle/sphere/hypersphere or outside ?





Ans : Circle also divides the region into two space , We will determine using below conditions :-

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Equation of a Ellipse(2D), Equation of Ellipsoid(3D), Equation of Hyper-Ellipsoid(n-D):

Ellipse are not much more used in ML , generally we used planes & circles.

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Square & Rectangle :

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